A Skew Symmetric Matrix or Anti-Symmetric Matrix is a square matrix whose transpose is negative to that of the original matrix. If the entry in the ith row and jth column of a matrix is a[i][j], i.e. if A = (a[i][j]) then the skew symmetric condition is -A = -a[j][i].
Examples :
Input : matrix: 0 5 -4
-5 0 1
4 -1 0
Output:
Transpose matrix: 0 -5 4
5 0 -1
-4 1 0
Skew Symmetric matrix
Approach:
- Find the transpose of the input matrix.
- If the input matrix is equal to the negative of its transpose matrix, then the matrix is Skew Symmetrical.
Below is the implementation of the above approach:
Java
// java program to check// whether given matrix// is skew-symmetric or notimport java.io.*;class GFG { static int ROW =3;static int COL =3;// Utility function to create transpose matrix static void transpose(int transpose_matrix[][], int matrix[][]){for (int i = 0; i < ROW; i++) for (int j = 0; j < COL; j++) transpose_matrix[j][i] = matrix[i][j];}// Utility function to check skew - symmetric// matrix condition static boolean check(int transpose_matrix[][], int matrix[][]){ for (int i = 0; i < ROW; i++) for (int j = 0; j < COL; j++) if (matrix[i][j] != -transpose_matrix[i][j]) return false; return true;}// Utility function to print a matrix static void printMatrix(int matrix[][]){ for (int i = 0; i < ROW; i++) { for (int j = 0; j < COL; j++) System.out.print(matrix[i][j] + " "); System.out.println(); }}// Driver program to test above functionspublic static void main (String[] args) { int matrix[][] = { {0, 5, -4}, {-5, 0, 1}, {4, -1, 0}, }; int transpose_matrix[][] = new int[ROW][COL]; // Function create transpose matrix transpose(transpose_matrix, matrix); System.out.println ("Transpose matrix: "); printMatrix(transpose_matrix); // Check whether matrix is skew-symmetric or not if (check(transpose_matrix, matrix)) System.out.println("Skew Symmetric Matrix"); else System.out.println("Not Skew Symmetric Matrix"); }}// This code is contributed by vt_m. |
C++
// C program to check whether given matrix// is skew-symmetric or not#include <stdio.h>#include <stdlib.h>#define ROW 3#define COL 3// Utility function to create transpose matrixvoid transpose(int transpose_matrix[ROW][COL], int matrix[ROW][COL]){ for (int i = 0; i < ROW; i++) for (int j = 0; j < COL; j++) transpose_matrix[j][i] = matrix[i][j];}// Utility function to check skew - symmetric// matrix conditionbool check(int transpose_matrix[ROW][COL], int matrix[ROW][COL]){ for (int i = 0; i < ROW; i++) for (int j = 0; j < COL; j++) if (matrix[i][j] != -transpose_matrix[i][j]) return false; return true;}// Utility function to print a matrixvoid printMatrix(int matrix[ROW][COL]){ for (int i = 0; i < ROW; i++) { for (int j = 0; j < COL; j++) printf("%d ", matrix[i][j]); printf("\n"); }}// Driver program to test above functionsint main(){ int matrix[ROW][COL] = { {0, 5, -4}, {-5, 0, 1}, {4, -1, 0}, }; int transpose_matrix[ROW][COL]; // Function create transpose matrix transpose(transpose_matrix, matrix); printf ("Transpose matrix: \n"); printMatrix(transpose_matrix); // Check whether matrix is skew-symmetric or not if (check(transpose_matrix, matrix)) printf("Skew Symmetric Matrix"); else printf("Not Skew Symmetric Matrix"); return 0;} |
C#
// C# program to check// whether given matrix// is skew-symmetric or notusing System;class GFG {static int ROW =3;static int COL =3;// Utility function to// create transpose matrixstatic void transpose(int [,]transpose_matrix, int [,]matrix){for (int i = 0; i < ROW; i++) for (int j = 0; j < COL; j++) transpose_matrix[j,i] = matrix[i,j];}// Utility function to check // skew - symmetric matrix // conditionstatic bool check(int [,]transpose_matrix, int [,]matrix){ for (int i = 0; i < ROW; i++) for (int j = 0; j < COL; j++) if (matrix[i, j] != -transpose_matrix[i, j]) return false; return true;}// Utility function// to print a matrixstatic void printMatrix(int [,]matrix){ for (int i = 0; i < ROW; i++) { for (int j = 0; j < COL; j++) Console.Write(matrix[i, j] + " "); Console.WriteLine(); }}// Driver Codepublic static void Main () { int [,]matrix = {{0, 5, -4}, {-5, 0, 1}, {4, -1, 0},}; int [,]transpose_matrix = new int[ROW, COL]; // Function create transpose matrix transpose(transpose_matrix, matrix); Console.WriteLine("Transpose matrix: "); printMatrix(transpose_matrix); // Check whether matrix is // skew-symmetric or not if (check(transpose_matrix, matrix)) Console.WriteLine("Skew Symmetric Matrix"); else Console.WriteLine("Not Skew Symmetric Matrix"); }}// This code is contributed by anuj_67. |
Python3
# Python 3 program to check# whether given matrix# is skew-symmetric or notROW=3COL=3# Utility function to# create transpose matrixdef transpose(transpose_matrix,matrix): for i in range (ROW): for j in range(COL): transpose_matrix[j][i] = matrix[i][j] # Utility function to# check skew - symmetric# matrix conditiondef check(transpose_matrix,matrix): for i in range(ROW): for j in range(COL): if (matrix[i][j] != -transpose_matrix[i][j]): return False return True # Utility function to print a matrixdef printMatrix(matrix): for i in range (ROW): for j in range(COL): print(matrix[i][j]," ",end="") print() # Driver program to test above functionsmatrix= [ [0, 5, -4], [-5, 0, 1], [4, -1, 0], ]transpose_matrix=[[0 for i in range(3)] for j in range(3)]# Function create transpose matrixtranspose(transpose_matrix, matrix)print("Transpose matrix:")printMatrix(transpose_matrix)# Check whether matrix is# skew-symmetric or notif (check(transpose_matrix, matrix)): print("Skew Symmetric Matrix")else: print("Not Skew Symmetric Matrix")# This code is contributed# by Azkia Anam. |
Javascript
// Javascript Program to check whether given matrix is skew-symmetric or notvar n = 3, m = 3;var matrix = [[ 0, 5, -4 ], [ -5, 0, 1 ], [ 4, -1, 0 ]];var transpose_matrix = [[], [], []];var transpose=function(transpose_matrix, matrix){ for (var i = 0; i < n; i++) for (var j = 0; j < m; j++) transpose_matrix[j][i] = matrix[i][j];}// Utility function to check skew - symmetric// matrix conditionvar check=function(transpose_matrix,matrix){ for (var i = 0; i < n; i++) for (var j = 0; j < m; j++) if (matrix[i][j] != -transpose_matrix[i][j]) return false; return true;}// Utility function to print a matrixvar printMatrix=function(matrix){ for (var i = 0; i < n; i++) { for (var j = 0; j < m; j++) console.log(matrix[i][j]); console.log('\n'); }}transpose(transpose_matrix, matrix);console.log("Transpose matrix: \n");printMatrix(transpose_matrix); // Check whether matrix is skew-symmetric or notif (check(transpose_matrix, matrix)) console.log("Skew Symmetric Matrix");else console.log("Not Skew Symmetric Matrix");// This code is contributed by Sajal Aggarwal. |
Output
Transpose matrix: 0 -5 4 5 0 -1 -4 1 0 Skew Symmetric Matrix
Time complexity: O(ROW x COL).
Auxiliary Space: O(ROW x COL).
References : Wikipedia
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